Physical Sciences and Mathematics Commons^™

Counting Convex Sets On Products Of Totally Ordered Sets, Brandy Amanda Barnette

Masters Theses & Specialist Projects

The main purpose of this thesis is to find the number of convex sets on a product of two totally ordered spaces. We will give formulas to find this number for specific cases and describe a process to obtain this number for all such spaces. In the first chapter we briefly discuss the motivation behind the work presented in this thesis. Also, the definitions and notation used throughout the paper are introduced here The second chapter starts with examining the product spaces of the form {1; 2; : : : ;n} × {1; 2}. That is, we begin by analyzing …